An example of a direct multiplexed, rms (root means square) responding electronic display is the well-known liquid crystal display (LCD). In such a display, a nematic liquid crystal material is positioned between two parallel glass plates having electrodes applied to each surface in contact with the liquid crystal material. The electrodes typically are arranged in vertical columns on one plate and horizontal rows on the other plate for driving a picture element (pixel) wherever a column and row electrode overlap.
In rms-responding displays, the optical state of a pixel is substantially responsive to the square of the voltage applied to the pixel, i.e., the difference in the voltages applied to the electrodes on the opposite sides of the pixel. LCDs have an inherent time constant that characterizes the time required for the optical state of a pixel to return to an equilibrium state after the optical state has been modified by changing the voltage applied to the pixel. Recent technological advances have produced LCDs with time constants (approximately 16.7 milliseconds) approaching the frame period used in many video displays. Such a short time constant allows the LCD to respond quickly and is especially advantageous for depicting motion without noticeable smearing or flickering of the displayed image.
Conventional direct multiplexed addressing methods for LCDs encounter a problem when the display time constant approaches the frame period. The problem occurs because conventional direct multiplexed addressing methods subject each pixel to a short duration "selection" pulse once per frame. The voltage level of the selection pulse is typically 7-13 times higher than the rms voltages averaged over the frame period. The optical state of a pixel in an LCD having a short time constant tends to return towards an equilibrium state between selection pulses, resulting in lowered image contrast, because the human eye integrates the resultant brightness transients at a perceived intermediate level. In addition, the high level of the selection pulse can cause alignment instabilities in some types of LCDs.
To overcome the above-described problems, an "active addressing" method for driving rms responding electronic displays has been developed. The active addressing method continuously drives the row electrodes with signals comprising a train of periodic pulses having a common period T corresponding to the frame period. The row signals are independent of the image to be displayed and preferably are orthogonal and normalized, i.e., orthonormal. The term "orthogonal" denotes that, if the amplitude of a signal applied to one of the rows is multiplied by the amplitude of a signal applied to another one of the rows, the integral of this product over the frame period is zero. The term "normalized" denotes that all the row signals have the same rms voltage integrated over the frame period T.
During each frame period a plurality of signals for the column electrodes are calculated and generated from the collective state of the pixels in each of the columns. The column voltage at any time t during the frame period is proportional to the sum obtained by considering each pixel in the column, multiplying a "pixel value" representing the optical state (either -1 for fully "on", +1 for fully "off", or values between -1 and +1 for proportionally corresponding gray shades) of the pixel by the value of that pixel's row signal at time t, and adding the products obtained thereby to the sum. In effect, the column voltages can be derived by transforming each column of a matrix of incoming image data by the orthonormal signals utilized for driving the rows of the display.
If driven in the active addressing manner described above, it can be shown mathematically that there is applied to each pixel of the display an rms voltage averaged over the frame period, and that the rms voltage is proportional to the pixel value for the frame. The advantage of active addressing is that it restores high contrast to the displayed image because, instead of applying a single, high level selection pulse to each pixel during the frame period, active addressing applies a plurality of much lower level (2-5 times the rms voltage) selection pulses spread throughout the frame period. In addition, the much lower level of the selection pulses substantially reduces the probability of alignment instabilities. As a result, utilizing an active addressing method, rms responding electronic displays, such as LCDs utilized in portable radio devices, can display image data at video speeds without smearing or flickering. Additionally, LCDs driven with an active addressing method can display image data having multiple shades without the contrast problems present in LCDs driven with conventional multiplexed addressing methods.
A drawback to utilizing active addressing results from the large number of calculations required to generate column and row signals for driving an rms-responding display. For example, a display having 480 rows and 640 columns requires approximately 230, 400 (# rows.sup.2) operations simply for generation of the column values for a single column during one frame period. While it is, of course, possible to perform calculations at this rate, such complex, rapidly performed calculations necessitate a large amount of power consumption and a large amount of memory. Therefore, a method referred to as "reduced line addressing" has been developed.
In reduced line addressing, the rows of a display are evenly divided and addressed separately. If, for instance, a display having 480 rows and 640 columns is utilized to display image data, the display could be divided into eight groups of sixty (60) rows, which are each addressed for 1/8 of the frame time, thus requiring only 60 (rather than 480) orthonormal signals for driving the rows. In operation, columns of an orthonormal matrix, which is representative of the orthonormal signals, are applied to rows of the different segments during different time periods. During the different time periods, the columns of the display are driven with rows of a "transformed image data matrix", which is representative of the image data which has been previously transformed, as described above, utilizing the orthonormal signals. In reduced line addressing, however, the transformed image data matrix can be transformed using the smaller set of orthonormal signals, i.e., using 60 orthonormal signals rather than 480 orthonormal signals. More specifically, the image data matrix is divided into segments of 60 rows, and each segment is transformed in an independent transformation using the 60 orthonormal signals to generate the transformed image data matrix.
Using the reduced line addressing method as described, approximately 3,600, i.e., 60.sup.2' operations are required for generation of the column voltages for a single column during each segment time. Because the frame period has been divided into eight segments, the total number of operations for generation of the column voltages for a single column during the frame period is approximately 28,800, i.e., 8 * 3,600. Therefore, in the above-described example, generating column values for driving a single column of a 480.times.640 display over an entire frame period using reduced line addressing requires only an eighth of the operations necessary for column voltage generation when the display is addressed as a whole. It will be appreciated that the reduced line addressing method therefore necessitates less power, less memory, and less time for performance of the required operations.
However, displays driven using reduced line addressing methods often have visible discontinuities at the boundaries of the display segments. The discontinuities result from the fact that, during generation of the column voltages, the actual image data is quantized as it is transformed due to limitations of hardware and software for performing the transformation. Therefore, the rms voltage applied to each pixel during the frame period cannot exactly reproduce the original image data, although the loss in data is not noticeable within each display segment because the column voltages for the rows of image data within each segment have been generated in a single transformation. The pixels at the boundaries of each display segment, however, are driven with column voltages generated in different transformations. As a result, discontinuities are introduced at the boundaries of the display segments, and, when viewed by the human eye, the image may not flow smoothly from one display segment to the next.
Thus, what is needed is method and apparatus for reducing discontinuities at the boundaries of an active-addressed display driven using reduced line addressing methods.